In the current artificial intelligence (AI) era, the scale and quality of the dataset play a crucial role in training a high-quality AI model. However, often original data cannot be shared due to privacy concerns and regulations. A potential solution is to release a synthetic dataset with a similar distribution to the private dataset. Nevertheless, in some scenarios, the attributes required to train an AI model are distributed among different parties, and the parties cannot share the local data for synthetic data construction due to privacy regulations. In PETS 2024, we recently introduced the first Vertical Federated Learning-based Generative Adversarial Network (VFLGAN) for publishing vertically partitioned static data. However, VFLGAN cannot effectively handle time-series data, presenting both temporal and attribute dimensions. In this article, we proposed VFLGAN-TS, which combines the ideas of attribute discriminator and vertical federated learning to generate synthetic time-series data in the vertically partitioned scenario. The performance of VFLGAN-TS is close to that of its counterpart, which is trained in a centralized manner and represents the upper limit for VFLGAN-TS. To further protect privacy, we apply a Gaussian mechanism to make VFLGAN-TS satisfy an $(ε,δ)$-differential privacy. Besides, we develop an enhanced privacy auditing scheme to evaluate the potential privacy breach through the framework of VFLGAN-TS and synthetic datasets.

The activation functions are fundamental to neural networks as they introduce non-linearity into data relationships, thereby enabling deep networks to approximate complex data relations. Existing efforts to enhance neural network performance have predominantly focused on developing new mathematical functions. However, we find that a well-designed combination of existing activation functions within a neural network can also achieve this objective. In this paper, we introduce the Combined Units activation (CombU), which employs different activation functions at various dimensions across different layers. This approach can be theoretically proven to fit most mathematical expressions accurately. The experiments conducted on four mathematical expression datasets, compared against six State-Of-The-Art (SOTA) activation function algorithms, demonstrate that CombU outperforms all SOTA algorithms in 10 out of 16 metrics and ranks in the top three for the remaining six metrics.